Management Science · 1977 · 58 citations · 4 references
ComputingMathematicsForecastingStochastic ProcessesTime Series AnalysisForecasting MethodsKalman FilteringState-space ModelsTime Series ForecastingTime Series ModelingTime Series PredictionAdditive NoiseFilteringFiltering TheoryKalman Filter EstimationKalman Filter PredictionState Vector EstimationState Vector FormalismState Vector Formulation
Kalman filtering is applied to forecasting problems where a time series is modeled as a time‑varying mean composed of known functions with unknown coefficients. The authors model the series as a linear system whose state vector contains the unknown coefficients and current mean, and apply the Kalman Filter to optimally estimate this state. The Kalman Filter’s key benefit is its ability to accommodate time‑varying coefficients, as illustrated by forecasting examples.
This paper describes the use of the Kalman Filter in a certain ciass of forecasting problems. The time series is assumed to be modeled as a time varying mean with additive noise. The mean of the time series is assumed to be a linear combination of known functions. The coefficients appearing in the linear combination are unknown. Under such assumptions, the time series can be described as a linear system with the state vector of the system being the unknown parameters and present value of the mean of the process. The Kalman Filter can be used under these circumstances to obtain an “optimal” estimate of the state vector. One of the distinct advantages of the Kalman Filter is that time varying coefficients can be permitted in the model. Examples using the Kalman Filter in forecasting are presented.
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